What is the correct solution status for (x-y=2) and (2x-2y=5)?
Answer and explanation
Correct answer: No solution
Writing the equations in standard form gives \\(a_1=1,b_1=-1,c_1=-2\\) and \\(a_2=2,b_2=-2,c_2=-5\\). Thus, \\(a_1/a_2=1/2\\) and \\(b_1/b_2=(-1)/(-2)=1/2\\), but \\(c_1/c_2=(-2)/(-5)=2/5\\). Since \\(a_1/a_2=b_1/b_2\\) but \\(c_1/c_2\\) is different, the two lines are parallel and distinct, so they have no solution. Exam tip: for an inconsistent pair, the first two coefficient ratios are equal while the constant-term ratio is different.
Frequently asked questions
What is the correct answer to this question?
No solution
Why is this the correct answer?
Writing the equations in standard form gives \\(a_1=1,b_1=-1,c_1=-2\\) and \\(a_2=2,b_2=-2,c_2=-5\\). Thus, \\(a_1/a_2=1/2\\) and \\(b_1/b_2=(-1)/(-2)=1/2\\), but \\(c_1/c_2=(-2)/(-5)=2/5\\). Since \\(a_1/a_2=b_1/b_2\\) but \\(c_1/c_2\\) is different, the two lines are parallel and distinct, so they have no solution. Exam tip: for an inconsistent pair, the first two coefficient ratios are equal while the constant-term ratio is different.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Conditions for solvability.
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